Computer-aided design of bi-ellipse bicycle sprocket

In cycling, pedaling is a combination of two pedal strokes by the left and right legs with different power. The pedaling power is transmitted from the human leg to the bike through the sprocket mechanism. However, research on sprocket design that considers the combination of two pedal strokes is limited. This paper proposes a CAD method to design a bi-ellipse sprocket that combines half different ellipses. The ellipses combination is used to accommodate the different torque between two pedals. Here, we built a sprocket prototype by adjusting the two vertical axes ratio on the bi-ellipse sprocket to be equal to the maximum torque ratio on the left and right crank. Then, we performed a pedaling comparison test between the circular sprocket and bi-ellipse sprocket prototype at the same rear-wheel rotational speed using a mountain bicycle mounted on an indoor bike trainer. In the test, the bi-ellipse prototype was also set up in eight different positions to the crank. Crank meter systems were installed on the bike to obtain the pedaling torque data and the pedaling power data on the left and right crank every 0.005 seconds. The result showed that the comparison parameter related to crank torque and power had smaller values on the bi-ellipse prototype than pedaling on the circular sprocket. Moreover, the asymmetry index of maximum torque in a specific position on the crank was lower than the circular sprocket. It can be concluded that using the bi-ellipse sprocket prototype makes pedaling more efficient, lighter, and safer to use. The proposed method can also be used as a guidance procedure to make countless bi-ellipse sprocket models.